The two-vehicle crash happened on the Belfast Road near the Derrycraw Road junction in Newry, Co Down shortly before 9.30 am.
Three policemen were injured but not seriously.
As a result of the fatal crash, the A1 road is closed between the Outlet centre at Banbridge and Sheepbridge Road.
Motorists are asked to avoid the area due to long tailbacks.
It is understood the nuns were on their way to the Dromantine Retreat and Conference Centre on the outskirts of Newry when the crash happened.
The police ombudsman is investigating the incident.
The PSNI’s Collision Investigation Unit is also at the scene.